Let's solve each of the problems step-by-step.
Question 4: Find the difference: \( \frac{3}{4} - \frac{2}{6} \)
To subtract these fractions, we need to find a common denominator. The denominators are 4 and 6. The least common multiple (LCM) of 4 and 6 is 12.
Now, convert each fraction:
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Convert \( \frac{3}{4} \): \[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]
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Convert \( \frac{2}{6} \): \[ \frac{2}{6} = \frac{2 \times 2}{6 \times 2} = \frac{4}{12} \]
Now we can subtract: \[ \frac{9}{12} - \frac{4}{12} = \frac{5}{12} \]
So, the answer is \( \frac{5}{12} \).
Question 5: Find the sum: \( \frac{4}{6} + \frac{2}{3} \)
Again, let's find a common denominator. The denominators are 6 and 3. The least common multiple of 6 and 3 is 6.
Convert \( \frac{2}{3} \) to have the same denominator of 6: \[ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \]
Now we can add: \[ \frac{4}{6} + \frac{4}{6} = \frac{8}{6} \]
Now, simplify \( \frac{8}{6} \): \[ \frac{8}{6} = \frac{4}{3} = 1 \frac{1}{3} \]
So, the answer is \( 1 \frac{1}{3} \).
Final Answers:
- \( \frac{5}{12} \) for the difference.
- \( 1 \frac{1}{3} \) for the sum.